MinT - Best Known (140−41, 140, s)-Nets in Base 2

Best Known (140−41, 140, s)-Nets in Base 2

(140−41, 140, 84)-Net over F₂ — Constructive and digital

Digital (99, 140, 84)-net over F₂, using

1 times m-reduction [i] based on digital (99, 141, 84)-net over F₂, using
- trace code for nets [i] based on digital (5, 47, 28)-net over F₈, using
  - net from sequence [i] based on digital (5, 27)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 5 and N(F) ≥ 28, using
      - a function field by SÃ©mirat [i]

(140−41, 140, 141)-Net over F₂ — Digital

Digital (99, 140, 141)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−41, 140, 997)-Net in Base 2 — Upper bound on s

There is no (99, 140, 998)-net in base 2, because

1 times m-reduction [i] would yield (99, 139, 998)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 701940 690139 100538 817410 846413 052687 370826 > 2¹³⁹ [i]